This lecture aims at introducing the notion of asymptotic symmetries in gravity and the derivation of the related surface charges by means of covariant phase space techniques. First, after a short historical introduction, I will rigorously define what is meant by “asymptotic symmetry” within the so-called gauge-fixing approach. The problem of fixing consistent boundary conditions and the...

We begin by reviewing the role of coadjoint orbits in the representation theory of nilpotents groups and then, to connect with the recent applications in physics of coadjoint orbits "around the corner" of the mathematical framework developed by Kirillov, we review the classification of coadjoint orbits of the Virasoro group. This will allow us to connect with more recent developments,...

Speaker Order:

Ankit Aggarwal, University of Amsterdam

Monireh Ahmadpour, University of Tehran

Giovanni Canepa, Centre de Physique Théorique

Roukaya Dekhil, Ludwig Maximilian University

Arnaud Delfante, University of Mons

Florian Ecker, Technische Universität Wien

Gloria Odak, Centre de Physique Théorique

In this introductory talk, I will present a new perspective about quantum gravity which is rooted deeply in a renewed understanding of local symmetries in Gravity that appears when we decompose gravitational systems into subsystems.

I will emphasize the central role of the corner symmetry group in capturing all the necessary data needed to glue back seamlessly quantum spacetime regions. I...

The goal of this talk is to discuss residual gauge symmetries in electromagnetism and gravity in Dirac's front form. Working in the light-cone gauge, I will demonstrate how the large gauge transformations and BMS supertranslations may be obtained from residual gauge invariance of the Hamiltonian action. The residual gauge symmetries in this (2+2) formulation share some striking similarities...

The flat space holography program aims at describing quantum gravity in asymptotically flat spacetime in terms of a dual lower-dimensional field theory. Two different roads to construct flat space holography have emerged. The first consists of a 4d bulk / 3d boundary duality, called Carrollian holography, where 4d gravity is suggested to be dual to a 3d Carrollian CFT living on the null...

I will present an analysis of the Hamiltonian formulation of gauge theories on manifolds with corners in the particular, yet common, case in which they admit an equivariant momentum map.

In the presence of corners, the momentum map splits into a part encoding “Cauchy data” or constraints, and a part encoding the “flux” across the corner. This decomposition plays an important role in the...

This talk reviews the use of radial quantization to compute Chern-Simons partition functions on handlebodies of arbitrary genus. The partition function is given by a particular transition amplitude between two states which are defined on the Riemann surfaces that define the (singular) foliation of the handlebody. By requiring that the only singularities of the gauge field inside the...

Corner symmetries are those diffeomorphisms that become physical in codimension two, in that they support non-zero Noether charges. Recently we have shown how to extend phase space so that all such charges are integrable and give a representation of the corner symmetry algebra on this extended phase space. More recently we have studied the coadjoint orbits of what we now call the universal...

The tree-level soft theorems were recently shown to arise from the conservation of infinite towers of charges extracted from the asymptotic Einstein equations. There is evidence this tower promotes the extended BMS algebra to an infinite higher-spin symmetry algebra. In this talk I will introduce towers of canonically conjugate memory and Goldstone operators, highlighting their role in...

The phase space of gravity restricted to a subregion bounded by a codimension-2 corner possesses an infinite-dimensional symmetry algebra consisting of diffeomorphisms of the 2-sphere and local SL(2,R) transformations of the normal planes. I will describe a deformation of a subalgebra preserving an area form on the sphere, and show that it leads to the finite dimensional algebra SU(N,N),...

I will review the recent construction of an extended solution space for gravity, based on a so-called partial Bondi gauge fixing. This aims at investigating the possible relaxations of the boundary conditions, in order to include for example a cosmological constant, a polyhomogeneous expansion, and an arbitrary time-dependent boundary metric. I will also explain how to properly map these...

In this talk, I will present an updated account on the prescription for BMS fluxes in asymptotically flat spacetimes, including their split into hard and soft pieces and the associated symplectic structure. Implications for flat space holography will be discussed.

In this talk, I will describe celestial higher spin charges as corner integrals, and their relationship with gravitational multipole moments. I will then explain that these charges uniquely label gravitational vacua and the corresponding flux-balance equations describe the transition caused by gravitational radiation among different vacua. This tak is based on arXiv:2206.12597.

We analyze, first from a geometric point of view, the behavior

of dynamical horizons. We then connect with Carrolian fluids and discuss potential phenomena stemming from non-linearities

in the resulting equations

[This is joint work with Jaime Redondo Yuste]

We construct a Hermitian random matrix model that provides a stable non-perturbative completion of Cangemi-Jackiw (CJ) gravity, a two-dimensional theory of black holes in asymptotically flat spacetimes. The matrix model reproduces, to all orders in the topological expansion, the Euclidean partition function of CJ gravity with an arbitrary number of boundaries. The non-perturbative completion...

This talk focuses on classical features of asymptotic QED, i.e. the limit of QED at null and time-like infinity. The BV-BFV formalism allows one to view this as a boundary theory of bulk QED and carries a natural notion of what it means to be a symmetry of the model. I will make the connection between this perspective and the earlier findings of Herdegen (JMP 1996) and Strominger et.al. (JHEP...

After reviewing the constrained Hamiltonian analysis of geometric actions, the construction is applied to the case of the BMS group in four dimensions, where it yields two plus one dimensional BMS4 invariant field theories. (Based on work done in collaboration with K. Nguyen and R. Ruzziconi)

On Tuesday, M. Schiavina laid out the theoretical framework for the symplectic reduction of gauge theories in the presence of corners. In this talk I will apply this theoretical framework to Yang-Mills theory on a null boundary and show how a pair of soft charges controls the residual (corner) gauge symmetry after the first-stage symplectic reduction, and therefore the superselection structure...

In this talk I will explore the role of the boundary Cotton tensor in the reconstruction of the solution space of four-dimensional asymptotically AdS and mostly asymptotically flat spacetimes. I will discuss charges from a purely boundary perspective, which emerge in sets of electric and magnetic towers, not necessarily conserved and possibly including subleading components.

In this talk, I will discuss certain homogeneous spaces of the Poincaré group that correspond to the well-known asymptotic regions of asymptotically flat spacetimes: time-, space-, and light-like infinity. I will then show that all of these spaces admit a uniform description as surfaces embedded in a higher-dimensional space. I will conclude with some comments concerning the computation of...

In the last few years, various authors have extended the covariant phase space to include arbitrary anomalies, and a notion of improved Noether charge. After reviewing this construction and discussing examples of anomalies, I will point out that the covariance requirements of the seminal Wald-Zoupas paper permit the presence of a special class of anomalies. To illustrate the meaning of such...